Question

A mark placed on the surface of a sphere is viewed through glass from a position directly opposite as shown in the figure. The diameter of the sphere is $30cm$ and refractive index of glass is $1.5$. The position of the image is

Answer 1

The focal length of the lens is,

$f=\frac{nr}{2(n-1)}=\frac{1.5\times 15}{2\times 0.5}=22.5$

Now the object distance, $u=15cm$ so image distance is,

$v=\frac{fu}{f-u}=\frac{22.5\times 15}{22.5-15}=45cm$

So image will be formed $45cm$ away from the center.